Appendix 310 A Implementation Details 311 In this section, we describe the implementation details of our algorithm for training on the training

We utilize the official implementation of TD-MPC [11] and MoDem [8] To update the SAE, we collect online data using a buffer with a size of 256. The following is the network architecture of the first STN block inserted into the encoder of TD-MPC. The following is the network architecture of the first STN block inserted into the encoder of MoDem. Hyperparameter V alue Discount factor 0.99 Image size 84 84 (TD-MPC) 224 224 (MoDem) Frame stack 3 (TD-MPC) 2 (MoDem) Action repeat 1 (xArm) 2 (Adroit, Finger, and Walker in DMControl) 4 (otherwise) Data augmentation 4 pixel image shifts (TD-MPC) 10 pixel image shifts (MoDem) Seed steps 5000 Replay buffer size Unlimited Sampling technique PER ( α = 0.6, β = 0.4) Planning horizon 5 Latent dimension 50 Learning rate 1e-3 (TD-MPC) 3e-4 (MoDem) Optimizer ( θ) Adam ( β The camera position varies continuously. For xArm, the mean of the distribution is 0, the standard deviation is 0.4, and we constrain the noise For DMControl, we modify the FOV from 45 to 53.